Here's a start on the lyrics, transcribed from listening to the sound track. I think most of it is right. I've put the parts I can't figure out in italics - they are sort of what I hear but I'm pretty sure the italicized words are wrong.

WHEN THE MOUNTAINS CRY

They lie like cold
On a poison thorn
In a dress
Dirty and torn
Young uns a-playin
As the black crow fly
Mamma's weepin
Hear the mountains cry.

There was another
A wilder part
Cold was her heart
And as dark as dark
Tears on the ground
Where her love did die
Neath the bloody moon
Hear the mountains cry.

Oh dig his grave
Narrow and deep
Set a jug of whiskey
By his thirsty feet
And lay two pennies
On his roving eye
Two women wailing
As the mountains cry.

Oh the wind blows weary
And the willows high
Rivers of sorrow
When the mountains cry,
Rivers of sorrow
When the mountains cry.
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Info from Masato's site:
Written by David Mansfield and Tom Russell
Published by Jocada Music (BMI) and Frontera Music (ASCAP)
Administered by Bug Music, Inc
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I found the simplicity of this song compelling in the movie but it's not so good on its own, especially when you have to listen to Aidan Quinn sing it.